Blender Orient an object (displaying Vector Arrows)
Consider a [Track To] constraint  which will rotate the arrow toward the location of a given target.  The green arrow points to the red ball below, wherever the ball happens to be.





In the animation below we see a few alternatives with constraints and modifiers





The blue arrow is a curve in case you find the straight lines excessively boring.  Circular cross section bevel. The curves has hook modifiers for the end points.  A third point is added into the blender curve to introduce more [visual curve] into the blender curve. The visual curve is optional. The green cap is position with a [follow path] constraint.  Of course this flexibility requires more work.
The yellow arrow is an array modifier fit to curve straight line
The large green arrow is the [track to] constraint as before
The hook constraints